A020755 Increasing gaps between squarefree numbers (upper end).

2, 5, 10, 51, 246, 849, 22026, 217077, 1092755, 8870033, 221167433, 47255689927, 82462576233, 1043460553378, 79180770078563, 3215226335143234, 23742453640900989, 125781000834058586

Offset

1,1

Comments

Up to n=10, a(n) is the upper end of the first gap of length n. However, for n=11 through n=16, a(n) is the upper end of the first gap of length n+1. See A020753. - M. F. Hasler, Dec 28 2015

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = A020754(n) + A020753(n). - M. F. Hasler, Dec 28 2015

Example

The first gap in A005117 occurs between 1 and 2 and has length 1. The next largest gap occurs between 3 and 5 and has length 2. The next largest gap is between 7 and 10 and has length 3. Etc. We are only interested in gaps that set new records.

Prog

(PARI) A020755(n)=for(k=L=1, 9e9, issquarefree(k)||next; k-L>=n&&return(k); L=k) \\ M. F. Hasler, Dec 28 2015

Crossrefs

Cf. A005117, A020754, A020753, A045882, A051681.

Sequence in context: A082593 A124664 A076776 * A378110 A018503 A018535

Adjacent sequences: A020752 A020753 A020754 * A020756 A020757 A020758

Keyword

nonn,hard

Author

David W. Wilson

Extensions

Thanks to Christian Bower for additional comments.

More terms (computed using data from A020754) added by M. F. Hasler, Dec 28 2015

Status

approved